3-Schurs from explicit representation of Yangian \(Y(\hat{\mathfrak{gl}}_1)\). Levels 1--5

DOI10.1007/JHEP11(2023)165arXiv2305.12282MaRDI QIDQ6183510

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Publication date: 26 January 2024

Published in: (Search for Journal in Brave)

Abstract: We suggest an ansatz for representation of affine Yangian

Y (h a t {m a t h f r a k g l}_{1})

by differential operators in the triangular set of time-variables

with

1 l e q s l a n t i l e q s l a n t a

, which saturates the MacMahon formula for the number of

3 d

Young diagrams/plane partitions. In this approach the 3-Schur polynomials are defined as the common eigenfunctions of an infinite set of commuting "cut-and-join" generators

p s i_{n}

of the Yangian. We manage to push this tedious program through to the 3-Schur polynomials of level 5, and this provides a rather big sample set, which can be now investigated by other methods.

Full work available at URL: https://arxiv.org/abs/2305.12282

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